You will need two logs, 200 coins, a hammer, a saw, and at least two nails. The hammer and saw can be bought from the Construction master.
Bronze nails can be made from a single bronze bar with at least 4 Smithing. Bring extras in case some are wasted.
Take the logs and coins to the sawmill east of Varrock, and have the logs cut into planks.
Visit your house in Building Mode and right-click on the chair hotspot in your parlour.
Choose to build a crude chair.
If your skill is higher you may build in any hotspot you wish to complete this task.

Rewards:

Completing this Task will earn you a sum of coins based on how many Tasks you have already done.